Keyless Entry System Malfunction

My fiancée and I both own relatively new Mazda's bought at the same time - hers is a 2019 MX-5 RF.
We were on vacation for a couple of weeks and when we returned, she initially received a Keyless Low Battery warning. She was able to start the car by placing her fob next to the start button and although she was able to go back and forth to her appointments, this error continued. A few days later (yesterday) when she jumped in her car, the car battery was completely dead. I tested it and it showed 3v - so I plugged in my trusty battery charger and let it charge overnight. Today, I replaced both fob batteries and again, we are still getting the Keyless Entry System Malfunction error and it also reports that the Key fob has a low battery. We were able to start the car, but we must still hold the fob next to the start button.

This is a relatively new 2019 car. Are the problems we are having associated with the car battery itself? It seems kind of crazy that a low mileage car battery from a 2019 model car would need replacing - and given that it was almost completely dead, I'm thinking it's telling me that there may be a short somewhere in the system.

Any thoughts and advice would be great... we both have appointments for our cars to be serviced next week (mine is a CX-5) so I think we can probably get it into the dealer on its own...
 
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2018 CX5 GT, Metallic Machine Gray and 2018 MX-5 RF GT, Soul Red
@jbphilli Re key fob... you may have a bad batch of batteries. I had purchased a 5 pack of Duracell replacements from Amazon and 3 of 5 batteries were duds. I wouldn’t think the key fob would be connected to the MX5 battery. It is still under warranty so have the dealer check the battery and alternator to see if the battery is being charged and holding a charge.

Wade
 
@jbphilli Re key fob... you may have a bad batch of batteries. I had purchased a 5 pack of Duracell replacements from Amazon and 3 of 5 batteries were duds. I wouldn’t think the key fob would be connected to the MX5 battery. It is still under warranty so have the dealer check the battery and alternator to see if the battery is being charged and holding a charge.

Wade
Thanks Wade - I think there are bigger issues. The battery was run down again and another error message showed up reflecting a "roof" malfunction. I disconnected the battery leads and have the car battery on a charger. Will charge it up for 2 days (since it's a slow charger) and if the car starts, and is drivable, we'll get it down to the dealer next week for its service appointment.
 
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2018 CX5 GT, Metallic Machine Gray and 2018 MX-5 RF GT, Soul Red
Hey jbphilli... let us know what the dealer says after they have looked at the issue.

Wade